Find the values of $x$ in each of the following:$ (13)^{\sqrt{x}}=4^{4}-3^{4}-6 $

Given:

\( (13)^{\sqrt{x}}=4^{4}-3^{4}-6 \)

To do: 

We have to find the value of $x$.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$(13)^{\sqrt{x}}=4^{4}-3^{4}-6$

$\Rightarrow (13)^{\sqrt{x}}=256-81-6$

$\Rightarrow (13)^{\sqrt{x}}=169$

$\Rightarrow (13)^{\sqrt{x}}=(13)^2$

Comparing both sides, we get,

$\sqrt{x}=2$

$\Rightarrow (\sqrt{x})^2=(2)^2$             [Squaring both sides]

$\Rightarrow x=4$

The value of $x$ is $4$.       

Tutorialspoint

Updated on: 10-Oct-2022

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